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Reverse Compose: Difference between revisions
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{{Built-in|Reverse Compose|⍛}} is a [[primitive operator]] closely related to [[Beside]] (< | {{Built-in|Reverse Compose|⍛}} is a [[primitive operator]] closely related to [[Beside]] (<syntaxhighlight lang=apl inline>∘</source>), which appears in [[Extended Dyalog APL]] and [[dzaima/APL]]. Called [[dyad|dyadically]] with function operands <syntaxhighlight lang=apl inline>f</source> and <syntaxhighlight lang=apl inline>g</source>, it uses <syntaxhighlight lang=apl inline>f</source> [[monad|monadically]] to pre-processes the left argument before applying <syntaxhighlight lang=apl inline>g</source> between the pre-processed left argument and the given right argument. <syntaxhighlight lang=apl inline>X f⍛g Y</source> is thus equivalent to <syntaxhighlight lang=apl inline>(f X) g Y</source>. The operator can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</source>. This dyadic definition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]]. | ||
Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], < | Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], <syntaxhighlight lang=apl inline>f⍛g Y</source> evaluated to <syntaxhighlight lang=apl inline>g Y</source>, but [[Adám Brudzewsky|Brudzewsky]]'s later Dyalog APL Vision defines<ref>[https://github.com/abrudz/dyalog_vision/blob/main/JotUnderbar.aplo JotUnderbar.aplo]</ref> it to be <syntaxhighlight lang=apl inline>Y f g Y</source>, matching Before. This later definition might also be written <syntaxhighlight lang=apl inline>f⍛g</source>{{←→}}<syntaxhighlight lang=apl inline>f⍛g⍨⍨</source>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</source>. In [[dzaima/APL]] the monadic case is simply an error. | ||
== Common usage == | == Common usage == | ||
Its plain usage is to pre-process left arguments without needing one or more applications of Commute (< | Its plain usage is to pre-process left arguments without needing one or more applications of Commute (<syntaxhighlight lang=apl inline>⍨</source>). For example, the square of the left argument minus the right argument can be expressed as: | ||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE4wPT3/Uu@JR72xdo///AQ Try it online!]< | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE4wPT3/Uu@JR72xdo///AQ Try it online!]<syntaxhighlight lang=apl> | ||
3×⍨⍛-2 | 3×⍨⍛-2 | ||
7 | 7 | ||
| Line 12: | Line 12: | ||
It can also be combined with Beside to create the [[split-compose]] construct. Here, we take the [[sign]] of the left argument and apply it to (that is, multiply it with) the absolute value of the right argument: | It can also be combined with Beside to create the [[split-compose]] construct. Here, we take the [[sign]] of the left argument and apply it to (that is, multiply it with) the absolute value of the right argument: | ||
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]< | [https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]<syntaxhighlight lang=apl> | ||
3 ¯1 4×⍛×∘|¯2 ¯7 1 | 3 ¯1 4×⍛×∘|¯2 ¯7 1 | ||
2 ¯7 1 | 2 ¯7 1 | ||